{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%matplotlib inline\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize']=(15,5)\n",
    "#%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(40,40,'$\\\\frac{\\\\alpha}{2}$')"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 求取绘制cdf的数据\n",
    "cdf_result=np.linspace(0,1,1000)\n",
    "x=norm.ppf(cdf_result)   # 求取不同cdf下对应的x值\n",
    "\n",
    "# 求取绘制pdf的数据\n",
    "xx=np.linspace(-4,4,500)\n",
    "yy=norm.pdf(x=xx,loc=0,scale=1)   # 求取不同xx下的概率密度值\n",
    "\n",
    "# 绘制相关图形\n",
    "fontdict = {'family': 'Times New Roman', 'weight': 'normal', 'size': 18}    #定义字体\n",
    "\n",
    "ax1=plt.subplot(121)\n",
    "ax1.plot(x,cdf_result)\n",
    "ax1.set_title('CDF',fontdict=fontdict)\n",
    "ax1.set_ylim((0,1))\n",
    "ax1.tick_params(labelsize=15)\n",
    "ax1.set_xlabel('(a)',fontdict=fontdict, labelpad=30)\n",
    "\n",
    "ax2=plt.subplot(122)\n",
    "ax2.plot(xx,yy)\n",
    "ax2.set_title('PDF',fontdict=fontdict)\n",
    "ax2.set_ylim((0,0.5))\n",
    "ax2.set_xlim((-4,4))\n",
    "ax2.tick_params(labelsize=15)\n",
    "ax2.set_xlabel('(b)',fontdict=fontdict, labelpad=16)\n",
    "\n",
    "# 求取分位数\n",
    "alpha=0.05\n",
    "x1=norm.ppf(alpha/2)\n",
    "x2=norm.ppf(1-alpha/2)\n",
    "pdf_x1=norm.pdf(x1)   #求取x1对应的概率密度\n",
    "\n",
    "# 绘制数轴中的tick\n",
    "plt.xticks([x1,x2,0],[r'$\\Phi^{-1}(\\frac{\\alpha}{2})$',r'$\\Phi^{-1}(1-\\frac{\\alpha}{2})$',0],fontsize=18)\n",
    "\n",
    "# 调整所有tick的字体\n",
    "labels = ax1.get_xticklabels() + ax1.get_yticklabels()+ax2.get_xticklabels() + ax2.get_yticklabels()\n",
    "[label.set_fontname('Times New Roman') for label in labels]\n",
    "\n",
    "# 在图2中绘制封闭区域，并标记相关区域\n",
    "ax2.fill_between(xx,yy,where=(yy<=pdf_x1),facecolor='blue')\n",
    "ax2.annotate(r'$\\frac{\\alpha}{2}$',xy=(x1-0.5, norm.pdf(x1-0.5)),xytext=(-40, 40),\n",
    "            textcoords='offset points', fontsize=20,\n",
    "            arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=.2\"))\n",
    "ax2.annotate(r'$\\frac{\\alpha}{2}$',xy=(x2+0.5, norm.pdf(x2+0.5)),xytext=(40, 40),\n",
    "            textcoords='offset points', fontsize=20,\n",
    "            arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=.2\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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